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This spring I planted 9 everbearing strawberries. Three were larger plants, six were smaller plants from the nursery.

The larger plants grew larger in size, did not send out any runners (I've read they don't send out as many as other types), and did not flower.

The smaller plants sent out some runners, flowered, and produced fruit.

Could the larger plants been older plants and less productive? I'm thinking about creating a strawberry specific box, so I was wondering if I should dig up the larger plants or keep them in the box another season?

I would keep them. In a plant's life cycle, it can "focus" on growing roots, flowering, fruiting and (in the case of strawberries) putting out runners. It could be that this particular plant has put down strong roots and you'll get a huge crop next year. Or not.